Mathematics – Functional Analysis
Scientific paper
1991-12-10
Arkiv Mat. 31, (1993), 13-26
Mathematics
Functional Analysis
Scientific paper
Let B denote an arbitrary Banach space, G a compact abelian group with Haar measure $\mu$ and dual group $\Gamma$. Let E be a Sidon subset of $\Gamma$ with Sidon constant S(E). Let r_n denote the n-th Rademacher function on [0, 1]. We show that there is a constant c, depending only on S(E), such that, for all $\alpha > 0$: c^{-1}P[| \sum_{n=1}^Na_nr_n| >= c \alpha ] <= \mu[| \sum_{n=1}^Na_n\gamma_n| >= \alpha ] <= cP [|\sum_{n=1}^Na_nr_n| >= c^{-1} \alpha ]
Asmar Nakhlé
Montgomery-Smith Stephen J.
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